A pseudo-octave is an interval whose frequency ratio is not 2:1, the definition of an octave, but is treated in some way or ways equivalent to this ratio. One example being the stretched octave: 2.1:1, which sounds out of tune played with harmonic overtones, but sounds strange but in tune when played with tones whose overtones are stretched equivalently, while the 2:1 octave then sounds out of tune. The octaves of Balinese gamelans are never tuned 2:1, but instead are stretched or compressed in a consistent manner throughout the range of each individual gamelan. Another example is the tritave of the Bohlen-Pierce scale.
See also